Apparatus for the measurement of plane surfaces



March 11,;1924. 11,486,203

H. THUN v M-"PARATUS FOR THE MEASUREMENT-OF PLANE SURFACES Filed Dec. 7.1920 Fate-med Mar. ii, 1%24.

r ar

HERMANNTHUILOF ESSEN, GERMANY, ASSIGNGR TO FRIED. KRUPP AKTIEINGESELL-SCHAFT, O33 ESSEN-ON THE-EUHR, GERMANY.

APPARATUS FOR THE IVLEASUB EIEG'LENT OF PLANE SURFACES.

Application filed December7y192fi. Serial No. 429,027.

To all whom it may concern:

Be it known that I, HERMANN THUN, residing at Essen, Germany, a citizenof the German Republic, have invented a certain new and usefulImprovement in Apparatus for the Measurement of Plane Surfaces, of whichthe following is a specification.

The present invention relates to an ap-- paratus for measuring planesurfaces, which is distinguished by a particularly advantageousconstruction and method of working.

A constructional example of the subject matter of the invention will bedescribed with reference to the accompanying drawings in which,

Figure 1 is a longitudinal elevation, partially in section of aconstruction according to this invention,

Figure 2 is a section on the line 22 of Fig. 1 looking from the right,and on a larger scale.

Figure 3 is a detail of Figure 1 partially in section and Figure 4 is adiagram which serves to explain the manner in which the apparatus works.

On a cylindrical column A (see Figure 1) which is provided at-the bottomwith a foot plate a and at the top with a handle (4 is mounted arotating sleeve B. The lower end of this sleeve B is fitted with alaterally projecting frame 6 and into an aperture 6 located in thelowerend of-the said sleeve B projects the point 0 (constructed in the formof a pivot pin) of a revolution paraboloid C, which has in its circularbase 0 an axial aperture 0 into which projects a pivot pin 6 carried bythe frame Z2 (see Figure 1). The longitudinal axis of the revolutionparaboloid C determined by the axes of the pivot pin 0 and the aperture0 cuts the axis of rotation of the sleeve B at right angles. The axis ofsymmetry of the generative parabola 0 of the revolution paraboloid Ccoincides with the axis of rotation of the column A. The apparatus is soconstructed that when the column A is placed with its foot plate a on afoundation or support, the paraboloid C just touches this foundation orsupport with the peripheral edge of its base in the man ner shown inFigures 1 and 2, so that when the sleeve B is rotated about the column Athe paraboloid C rotates on the foundation or support.

The sleeve B has a projection 6 (see Figures 1 and 2) to which isattached a rack D provided with teeth. (Z on its underside. Fitted tothe rack D is a longitudinally movable slide E, in which are mounted tworigidly united gear wheels f and f which are both carried and rotate onthe same shaft F. The gear wheels 7 gears into the teeth 611 of the rackD and the gear wheel 7 into the teeth 9 of a rack G which is movablelongitndinally in the slide E. The rack G is parallel with the rack Dand carries on one end a downwardly extending pin which is intended totravel round the portion of surfaces to be measured. A rectangularrecess 2) (see Figure 1) is rovided in the projection b for the otherend of the longitudinally movable rack G and acts as a guide therefor.

The slide E has a projection 0 in a ver tical opening of which arectangular bar H is slidably guided, and on the lower end of the bar His mounted a hollow block h in which is mounted and rotates a worm i(see Figures 2 and 3). The worm shaft has one end projecting from theblock h and a friction wheel J is mounted thereon on which is inscribeda scale 2' The worm 5 gears into a worm wheel 70 also mounted in theblock k and having on the end of its shaft which projects from the blockb a wheel 'K, on which is inscribed a scale 70 Each of the scales 7? andk is provided with a reading off mark h and it respectively, inscribedon the block h. The divisions of the scales and lc 'have numbers (notshown) allotted to them which denote units of surface area. The frictionwheel J, hereinafter termed the measuring wheel, bears upon the outersurface of the paraboloid G and the arrangement of the several parts issuch that the axis of rotation of the measuring Wheel J lies in theplane including the axis of rotation of the sleeve B and parallel to theaxis of the paraboloid C. The mechanism actuated by'the wheel J andcarried by the block it is termed the registering mechanism and thismechanism and the Wheel together constitute the measuring mechanism.

For the purpose of illustrating the manner in which this apparatus forthe measure spending scales z' -and rack G to any desired point m on theboundary line m of the surface to be measured. During this longitudinalmovement of the rack G the slide E is moved longitudinally by means ofthe toothed wheel gearing 9 f 7, al on the rack D mounted on the sleeveB, and the ratio of transmission of this toothed Wheel gearing is suchthat the ratio of the distances (denoted in Figure 1, by R and R of themeasuring wheel J and the pin 9 from the axis of rotation of the sleeveB emains constant.

The'measuring operation is now carried out by guiding the pin 9(starting from the point m in one and the same direction round theboundary line m of the surface to be measured. During this guiding ofthe pin 9 both a longitudinal and a rotary movement of the rack G areproduced.

For the purposes of further comprehension of the working of thisapparatus let it be supposed that the surface to be measured is dividedup into an infinite number of elementary triangles With equal angles atthe center, all of which proceed from the point M and of which two areshown on an enlarged scale in the drawing. The area of each of theseelementary triangles is propor tional to the square of the radius R,(see Figure 4) corresponding to this triangle proceeding from the pointM and bisecting the angle at the center.

The operations which take place while the pin g is guided from the pointm to the point m of the boundary line m will first be described; Inconsequence of the longitudinal movement of the rack D which takes placeduring this guiding'of the pin 9 the slide Emoves along the rack D andconsequently the'measuring Wheel J is moved on the outer surface of theparaboloid C in an axial direction. The radius R (see Figure l) of itspoint of contact with the outer surface of the paraboloid C is at thesame time, asthe relationship R :R :a constant already mentioned stillexists, proportional to the square of R (see Figures 1 and 4) accordingto the equation which applies for the generatrix of the paraboloid C.

In consequence of the rotary movement of the rack G, which takes placeWhen the pin 5/ is guided in the manner above described, the sleeve Withall the parts mounted upon it is rotated round the axis of the column Aand at the same time the paraboloid C, rotating about the axisdetermined by the pin 0 and the aperture 0 rolls over the foundation orsupport. This rolling of the paraboloid C causes the measuring Wheel 'Jto turn also and the amount of turning of the measuring Wheel J is alinear function of the radius B and consequently a quadratic function ofthe distance of the pin 9 from the axis of rotation of the sleeve B,Which is denoted by 3,. Since, as has already been stated, the area ofthe elementary triangle determined by the points M,'m and m isproportional .to the square of the distance R and consequently is also aquadratic function of the distance R the an gular path traversed by themeasuring wheel J forms directly a measure of the elementary tianglewhichis determined by the points M, m m

The scales 2' and is which take part in the rotary movement of themeasuring wheel J are .so numbered that the area of the elementarytriangle can be read off by means ofthere is addedto the angulanpathalready traversed by the measuring Wheel J an an- 7 gular path which isa measure of the elementarytriangle determined by the points M, m m Thearea of the two elementary triangles M, m m and M, m M can there forenow be read off 011 the reading off device formed by the scales 2' and kandthe marks If and 7L3. On guidmg the pin 9 still further along theseries'of lines m the areas of the elementary triangles passed throughwill be added in a similarmanner to the the point m the reading offdevice z'flh 73 7&3 indicates the sum of the areas of all the elementarytriangles in the surface included in or bounded by the series of lines mor in other words indicates the area of this surface. 7

It can be proved that the area of the sur 7 face bounded by the seriesof linesm can be determined by passing round it once, if the column A beplaced on a point M (see Figure 4-) outside the surface to be meas- .inground the series of lines m in the direction of rotation above given,the pin 9 is guided on the line m to the series of lines m and afterhaving been passed round the series of lines m in the reverse direction,is again returned on the line m to the point m An important advantage ofthe apparatus forming the subject of the present invention results fromthe fact that the member (i. e. the paraboloid C) which drives thereading of apparatus travels over an arc of a circle, the centre pointof which does not change during the measuring operation, whereby it ispossible to see at once whether the point selected for the position ofthe apparatus will enable the measuring operation to be carried out ornot. Also another and very important advantage is that in comparisonwith known surface measuring appliances there are no positions for thecolumn A of the machine which are capable of causing an error in theresult of the measurement. For this reason therefore no specialattention need be paid to the selection of the point on which theapparatus is set up.

Claims:

1. An apparatus for the measurement of plane surfaces comprising atracer pin adapted to be moved around the surface to be measured, acolumn, means connecting said tracer pin to said column whereby saidtracer pin may be moved radially to and circumferentially about saidcolumn, a registering device, a measuring wheel operatively connectedthereto, a paraboloid, means whereby said paraboloid is revolublysupported to roll in contact with said measuring wheel and with a fixedsurface about an aXis which is radial to said column and is constrainedto move thereabout in accordance with the circumferential movements ofsaid tracer pin, means connecting said first named connecting means tosaid measuring wheel so that when the tracer pin is moved around thesurface to be measured the wheel will be so positioned radially that therotation imparted thereto by said paraboloid is a quadratic function ofthe distance of said tracer pin from said column.

2. An apparatus for the measurement of plane surfaces comprising acolumn, a carrier rotatably mounted on said column, a slide supported bysaid carrier to move at right angles to the axis of the column, a tracerpin supported by said slide, a measuring wheel mounted to move with saidslide, a revolving paraboloid mounted on said carrier with its axis atright angles to that of said column, said paraboloid being adapted toroll upon a fixed surface when said carrier is rotated and saidmeasuring wheel being adapted for rolling on the outer surface of saidparaboloid.

3. An apparatus adapted for measuring plane surfaces comprising arotatably mounted carrier, a slide supported thereby to move at rightangles to the axis of rotation of the carrier, a tracer pin, means forsupporting said tracer pin from said carrier whereby the pin will bemoved circumferentially with the carrier but may be moved radially withreference thereto, a. measuring wheel and registering mechanism mountedto' move with the slide, the wheel being adapted to actuate saidmechanism, a revolving paraboloid supported by said carrier and adaptedto revolve by contact with a fixed surface when said carrier is rotated,said measuring wheel contacting with said paraboloid to cause saidregistering mechanism to function, for the purpose of indicating thearea of the measured surface.

4. An apparatus of the class described adapted for measuring planesurfaces comprising a rotatab y mounted carrier, a rack radiallyprojecting therefrom, a slide supported on the rack and movabletherealong, a radially movable rack supported by said carrier, a tracerpin carried by the end of said last named rack, a measuring meansincluding a measuring wheel supported by said slide, a connectionbetween said first mentioned rack, said slide and said longitudinallymovable rack whereby the ratio of the distances of the measuring wheeland of the tracer pin from the axis of rotation of the carrier ismaintained constant.

5. An apparatus for the measurement of plane surfaces comprising atracer p-in, means forming a pole or pivot, means connecting said tracerpin to said pivot where by said pin is adapted for movement radially tosaid pivot and circumferentially about it, a registering device, ameasuring wheel operatively connected to said device, anaxially-elongated rolling body, circular in cross section and comprisinga paraboloid, means supporting said body whereby its axis is maintainedradial to said pivot and is controlled to swing about it in accordancewith the circumferential movements of the tracer pin, the body beingthus adapted for rolling upon a fixed surface and about the pivot, andmeans for so connecting said measuring wheel to a part of saidpin-and-pivot-connecting means that the wheel will be maintained inrolling contact with the paraboloid and will be so bodily moved axiallytherealong, by the radial movements of the pin, as it is caused to tracethe outlines of the area being measured, that the revolutions impartedto the wheel by the resulting roll-' ing of the elongated body will be aquadratic function of the distance of said pin from the axis of thepivot.

6. A polar planimeter comprising a frame adapted to turn about a poleperpendicular to the surface to be measured, an outline tracing pointer,means whereby said pointer is guided by the frame for movement relativethereto in a straight path directed sub stantially towards the pole, andarea-registering means adapted for actuation upon pivotal movement oftheli'ame overa stationary surface by rolling contact of one of theelements of the means with said surface, said means including an axiallyelongated pivoted member mounted in the frame With its axis radial tothe pole and substantially parallel tothe path of movement of thepointer, said member being so actuated as torotate in harmony with anycircumferential movement of the pointer about the pole, saidarea-registering means also including a friction Wheel mounted forrolling contact with said'member and for bodily movement lengthwisethereof and means whereby said bodily movement is controlled by thepointer to be in harmony with the movement of the latter radial tothepole, said axially elon gated member being circular in cross-sectionand so varying in size along its axis that for any plane of contactWiththe Wheel its di-' ameter will bear a fixed ratio to the square ofthe corresponding distance of the pointer from the pole. V

The foregoing specification signed at Essen, Germany, this 17th day ofAugust, 1920.

HERMANN 'THUNQ In presence of-- v HANS GO'ITSMANN, CARL MfiLLER,

